Certainly! Let's break down the problem step by step.
### Problem:
1. First Item:
- Cost before tax: $232
- Sales tax amount: $16
2. Second Item:
- Sales tax amount: $22
- Find the cost before tax for this item.
### Solution:
#### Step 1: Determine the sales tax percentage.
To find the sales tax percentage, we use the information given for the first item. The formula for calculating the sales tax percentage is:
[tex]\[ \text{Sales Tax Percentage} = \left( \frac{\text{Sales Tax Amount}}{\text{Cost Before Tax}} \right) \times 100 \][/tex]
Plugging in the values for the first item:
[tex]\[ \text{Sales Tax Percentage} = \left( \frac{16}{232} \right) \times 100 \approx 6.896551724137931\% \][/tex]
So, the sales tax percentage is approximately 6.896551724137931%.
#### Step 2: Calculate the cost before tax for the second item.
We know that the sales tax amount for the second item is $22 and we have calculated the sales tax percentage.
To find the cost before tax for the second item, we use the formula:
[tex]\[ \text{Cost Before Tax} = \frac{\text{Sales Tax Amount}}{\text{Sales Tax Percentage} / 100} \][/tex]
Plugging in the values:
[tex]\[ \text{Cost Before Tax} = \frac{22}{6.896551724137931 / 100} \][/tex]
[tex]\[ \text{Cost Before Tax} = \frac{22}{0.06896551724137931} \][/tex]
[tex]\[ \text{Cost Before Tax} \approx 319 \][/tex]
So, the cost before tax for the second item is $319.00.
### Summary:
- The sales tax percentage is approximately 6.896551724137931%.
- The cost before tax for the second item is $319.00.
This completes our step-by-step solution.
